At the end of Harvey's Revised English Grammar (1878) is a system which looks similar to R-K diagrams, but which is greatly simplified, in what appears to be unfortunate ways. Visually, note the absence of R-K's slanting lines for modifiers. Also, notice that the various modifiers are, in many cases, not clearly separated.

Sample diagrams for complex sentences, showing content clauses, infinitives, etc. (pp. 268-269)

The last page of this volume contains a plug for another book of diagrams by the same publisher: Irish's Grammar and Analysis Made Easy and Attractive by Diagrams. Given the nature of the diagrams in Harvey's Grammar, I suspect that this diagram system was cribbed from Reed and Kellogg, with enough changes to avoid copyright problems.

1. “In the beginning God created the heaven and the earth.”

(14.)

1. “The king of shadows loves a shining mark.”

(13.)

Rem.—Some sentences assert the being, condition, or state, of a person or thing—or an action which does not terminate on an object. Others assert an ction which terminates on an object.

Some sentences assert but one fact; others, more. Some assert an independent, or a principal proposition; others, a secondary, or qualifying proposition. Hence,

Prin. Sentences are distinguished as—

Prin. The office of a word in a sentence, determines its position in the diagram, according to the following

RULE

1. The principal parts of a sentence are placed uppermost, and on the same horizontal line; as 1, 2, 3.
2. The Subject of a sentence takes the first place; as 1.
3. The Predicate is placed to the right of the subject—attached; as 2—7—11—26
4. The Object is placed to the right of the predicate; as 3. The object of a phrase is placed to the right of the word which introduces the phrase; as 22 to the right of 21.
5. A word, phrase, or sentence, is placed beneath the word which it qualifies; as 4 and 5 qualify I ~—(25, 26, x) qualify 22
6. A word used to introduce a phrase, is placed beneath the word which the phrase qualities—having its object to the right and connecting both; as 15 connecting 12 and 16—21 connecting 3 and 22.
7. A word used only to connect, is placed between the two words connected; as 10 between 7 and 11; and a word used to introduce a sentence, is placed above the predicate of the sentence, and attached to it by a line; as 0 above 2.
8. A word relating back to an other word, is attached to the antecedent by a line; as 6 attached to 1, and x to 22.

The first complete diagramming system was developed by S. W. Clark in A Practical Grammar: in which Words, Phrases, and Sentences are Classified According to their Offices, and their Relation to Each Other. Illustrated by a Complete System of Diagrams (1847). His system

In the United States there are currently two major varieties of diagrams in use to represent sentence structure: traditional diagrams, used more or less exclusively in junior high school and high school classrooms, and tree diagrams, the most common method used by professional linguists.

In traditional grammar, adverb was a catch-all category for everything that was difficult to analyze. Unfortunately, this had the effect of making the category heterogeneous. Some words that are traditionally called adverbs show very different distributions from other words in the same caategory. In some cases, we will not categorize these words as adverbs at all. We will note such cases as they occur in later chapters. We will begin, however, with the most obvious cases.

Adverbs are characteristically used to modify verbs. That is, they perform the same function for verbs that adjectives do for nouns. And indeed, adjectives and adverbs are often closely related, but they do not appear in the same function: